Cross-scale Modeling of Functional Grading in Musculoskeletal Tissues
Interfaces in physiology often present transitional zones with gradual changes in composition, structure, and mechanical properties. For example, the attachment between tendon to bone features a unique interfacial region that is critical for musculoskeletal physiological function. The proposed dissertation aims to identify, through mathematical modeling of graded tissue regions, the ways that these regions contribute to physiological function, and the ways that the degeneration of these regions contribute to pathology. The dissertation introduces new modeling tools for this purpose. By identifying physiological and pathophysiological roles of graded tissue regions, the results in this dissertation serves as a foundation for guiding novel strategies and tissue engineering approaches to repair of graded tissue regions. The dissertation contains three parts. First, we focused on the cross-scale, graded stiffening mechanisms that endow healthy the rotator cuff tendon-to-bone attachment with high resilience. Accumulation of a high volume fraction of mineral inclusions within and upon collagen fibers occurs in a graded fashion as tissue transitions from tendon to bone, but existing homogenization techniques that describe how stiffening emerges hierarchically are not suitable at these high volume fractions of inclusions. We therefore applied homogenization concepts to develop a theoretical method capable of estimating the effective elastic properties of composites containing a high volume fraction of different inclusion types. We applied this method to predict how tissue stiffness varies as a function of mineral volume fraction at the tendon-to-bone attachment, leading to a gradation in mechanical properties that alleviates stress concentrations. Next, we investigated these mechanisms of load transfer to resolve a paradox about the architecture of the rotator cuff, and provide further guidance to repair strategies. The gradation in tissue properties is believed to be central to load transfer, but how then could its absolute size be conserved across mammals spanning several orders of magnitude in size? By comparing morphology across species, we identified several surprising features of the attachment site. Most importantly, results suggested that morphological variation across species is optimized to conserve the macroscale stress concentration at the tendon- to-bone insertion site. Variation of parameters across species was relatively low for factors that strongly affect the stress concentration, and high for factors that do not. These results suggest ways that morphological features at the repaired attachment of tendon to bone that can be tailored across length scales to restore healthy load transfer following injury. Finally, we investigated the biomechanical role of the functionally graded peri-cellular matrix (PCM) surrounding chondrocytes such as those that appear in the fibrocartilaginous region of the attachment of tendon to bone, and in articular cartilage. Results supported a hypothesis that this functionally graded peri-cellular matrix (PCM) may serve as a tool for controlling surface signaling of these cells and the dilatation of the PCM, the latter being vital for the flow of nutrients. Together, the results highlight the role of gradients in physiology, and the role of mechanics in guiding tissue engineered strategies for repairing these gradients.
Mechanical Engineering, Osteopathic Medicine and Osteopathy
Networked Digital Library of Theses and Dissertations